Achille Brocot's original paper "Calcul des rouages par approximation, nouvelle methode", published in 1861 in "Revue Chronometrique. Journal des horlogers, scientifique et pratique" is available through Google books! You can read the journal or you can download it as a PDF (Brocot's paper goes from page 208 to 216 of the PDF file)

We derive an algorithm that enables the rationals to be enumerated in two different ways. One
way is known, and is called Calkin-Wilf-Newman enumeration; the second is new and corresponds to
a flattening of the Stern-Brocot tree of rationals. We show that both enumerations stem from
the same simple algorithm. In this way, we construct a Stern-Brocot enumeration algorithm with the
same time and space complexity as Calkin-Wilf-Newman enumeration.